Question: Simplify the following expression and state the condition under which the simplification is valid. $y = \dfrac{n^2 - 81}{n + 9}$
First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = n$ $ b = \sqrt{81} = 9$ So we can rewrite the expression as: $y = \dfrac{({n} + {9})({n} {-9})} {n + 9} $ We can divide the numerator and denominator by $(n + 9)$ on condition that $n \neq -9$ Therefore $y = n - 9; n \neq -9$